[Solved] Using normal distribution of the random variable X as an approximation of the binomial distribution, with parameters N=50 and P=2/3. Calculate


Question: Using normal distribution of the random variable X as an approximation of the binomial distribution, with parameters N=50 and P=2/3.

  1. Calculate the mean and standard deviation of X.
  2. By using this normal approximation, calculate P(30 < 40)
  3. If you perform this experiment nine times and calculate the average of the nine experiments \(\bar{X}\), calculate \(\Pr \left( 30<\bar{X}<40 \right)\)

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